The Hypotenuse Of A $45 {\circ}-45 {\circ}-90^{\circ}$ Triangle Measures $10 \sqrt{5}$ Inches.What Is The Length Of One Leg Of The Triangle?A. $ 5 5 5 \sqrt{5} 5 5 [/tex] B. $5 \sqrt{10}$ C. $10
Introduction to 45°-45°-90° Triangles
A 45°-45°-90° triangle is a special type of right-angled triangle where two angles are 45° each, and the third angle is 90°. This triangle has some unique properties that make it easier to work with. In this article, we will explore the relationship between the legs and the hypotenuse of a 45°-45°-90° triangle.
Properties of 45°-45°-90° Triangles
One of the key properties of a 45°-45°-90° triangle is that the two legs are equal in length. This means that if one leg is x inches long, the other leg is also x inches long. The hypotenuse, which is the side opposite the right angle, is √2 times the length of each leg.
The Relationship Between Legs and Hypotenuse
To understand the relationship between the legs and the hypotenuse, let's consider the following:
- If one leg is x inches long, the other leg is also x inches long.
- The hypotenuse is √2 times the length of each leg.
- Therefore, the length of the hypotenuse is x√2 inches.
Finding the Length of One Leg
Now, let's use the given information to find the length of one leg of the triangle. We are told that the hypotenuse measures 10√5 inches. We can set up an equation using the relationship between the legs and the hypotenuse:
x√2 = 10√5
To solve for x, we can divide both sides of the equation by √2:
x = 10√5 / √2
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2) × 1
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/2)
x = 10√(5/2) × √(2/2)
x = 10√(5/2) × √(1)
x = 10√(5/
Q&A: The Hypotenuse of a 45°-45°-90° Triangle
Q: What is a 45°-45°-90° triangle?
A: A 45°-45°-90° triangle is a special type of right-angled triangle where two angles are 45° each, and the third angle is 90°.
Q: What are the properties of a 45°-45°-90° triangle?
A: One of the key properties of a 45°-45°-90° triangle is that the two legs are equal in length. This means that if one leg is x inches long, the other leg is also x inches long. The hypotenuse, which is the side opposite the right angle, is √2 times the length of each leg.
Q: How do I find the length of one leg of a 45°-45°-90° triangle?
A: To find the length of one leg of a 45°-45°-90° triangle, you can use the relationship between the legs and the hypotenuse. If the hypotenuse is x√2 inches long, then the length of one leg is x inches.
Q: What is the relationship between the legs and the hypotenuse of a 45°-45°-90° triangle?
A: The relationship between the legs and the hypotenuse of a 45°-45°-90° triangle is that the hypotenuse is √2 times the length of each leg.
Q: How do I use the given information to find the length of one leg of the triangle?
A: To use the given information to find the length of one leg of the triangle, you can set up an equation using the relationship between the legs and the hypotenuse. If the hypotenuse measures 10√5 inches, then you can set up the equation x√2 = 10√5.
Q: How do I solve for x in the equation x√2 = 10√5?
A: To solve for x in the equation x√2 = 10√5, you can divide both sides of the equation by √2. This gives you x = 10√5 / √2.
Q: How do I simplify the expression x = 10√5 / √2?
A: To simplify the expression x = 10√5 / √2, you can multiply the numerator and denominator by √2. This gives you x = 10√(5/2).
Q: What is the final answer for the length of one leg of the triangle?
A: The final answer for the length of one leg of the triangle is 5√10.
Q: What is the relationship between the legs and the hypotenuse of a 45°-45°-90° triangle?
A: The relationship between the legs and the hypotenuse of a 45°-45°-90° triangle is that the hypotenuse is √2 times the length of each leg.
Q: How do I use the given information to find the length of one leg of the triangle?
A: To use the given information to find the length of one leg of the triangle, you can set up an equation using the relationship between the legs and the hypotenuse. If the hypotenuse measures 10√5 inches, then you can set up the equation x√2 = 10√5.
Q: How do I solve for x in the equation x√2 = 10√5?
A: To solve for x in the equation x√2 = 10√5, you can divide both sides of the equation by √2. This gives you x = 10√5 / √2.
Q: How do I simplify the expression x = 10√5 / √2?
A: To simplify the expression x = 10√5 / √2, you can multiply the numerator and denominator by √2. This gives you x = 10√(5/2).
Q: What is the final answer for the length of one leg of the triangle?
A: The final answer for the length of one leg of the triangle is 5√10.
Q: What is the relationship between the legs and the hypotenuse of a 45°-45°-90° triangle?
A: The relationship between the legs and the hypotenuse of a 45°-45°-90° triangle is that the hypotenuse is √2 times the length of each leg.
Q: How do I use the given information to find the length of one leg of the triangle?
A: To use the given information to find the length of one leg of the triangle, you can set up an equation using the relationship between the legs and the hypotenuse. If the hypotenuse measures 10√5 inches, then you can set up the equation x√2 = 10√5.
Q: How do I solve for x in the equation x√2 = 10√5?
A: To solve for x in the equation x√2 = 10√5, you can divide both sides of the equation by √2. This gives you x = 10√5 / √2.
Q: How do I simplify the expression x = 10√5 / √2?
A: To simplify the expression x = 10√5 / √2, you can multiply the numerator and denominator by √2. This gives you x = 10√(5/2).
Q: What is the final answer for the length of one leg of the triangle?
A: The final answer for the length of one leg of the triangle is 5√10.